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Data Communication and Networks
Lectures 8 and 9
Networks: Part 2Routing Algorithms and Routing Protocols
October 26, November 2, 2006
Fixed Routing
• Single permanent route for each source to destination pair
• Determine routes using a least cost algorithm
• Route fixed, at least until a change in network topology
Flooding
• No network info required• Packet sent by node to every neighbor• Incoming packets retransmitted on every link
except incoming link• Eventually a number of copies will arrive at
destination• Each packet is uniquely numbered so duplicates
can be discarded• Nodes can remember packets already forwarded
to keep network load in bounds• Can include a hop count in packets
Properties of Flooding
• All possible routes are tried—Very robust
• At least one packet will have taken minimum hop count route—Can be used to set up virtual circuit
• All nodes are visited—Useful to distribute information (e.g. routing)
Random Routing
• Node selects one outgoing path for retransmission of incoming packet
• Selection can be random or round robin• Can select outgoing path based on
probability calculation• No network info needed• Route is typically not least cost nor
minimum hop
Adaptive Routing
• Used by almost all packet switching networks• Routing decisions change as conditions on the
network change—Failure—Congestion
• Requires info about network• Decisions more complex• Tradeoff between quality of network info and
overhead• Reacting too quickly can cause oscillation• Reacting too slowly to be relevant
1
23
0111
value in arrivingpacket’s header
routing algorithm
local forwarding tableheader value output link
0100010101111001
3221
Interplay between routing and forwarding
u
yx
wv
z2
2
13
1
1
2
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5
Graph: G = (N,E)
N = set of routers = { u, v, w, x, y, z }
E = set of links ={ (u,v), (u,x), (v,x), (v,w), (x,w), (x,y), (w,y), (w,z), (y,z) }
Graph abstraction
Remark: Graph abstraction is useful in other network contexts
Example: P2P, where N is set of peers and E is set of TCP connections
Graph abstraction: costs
u
yx
wv
z2
2
13
1
1
2
53
5 • c(x,x’) = cost of link (x,x’)
- e.g., c(w,z) = 5
• cost could always be 1, or inversely related to bandwidth,or inversely related to congestion
Cost of path (x1, x2, x3,…, xp) = c(x1,x2) + c(x2,x3) + … + c(xp-1,xp)
Question: What’s the least-cost path between u and z ?
Routing algorithm: algorithm that finds least-cost path
Routing Algorithm classification
Global or decentralized information?
Global:• all routers have complete
topology, link cost info• “link state” algorithmsDecentralized: • router knows physically-
connected neighbors, link costs to neighbors
• iterative process of computation, exchange of info with neighbors
• “distance vector” algorithms
Static or dynamic?Static: • routes change slowly
over timeDynamic: • routes change more
quickly—periodic update—in response to link
cost changes
A Link-State Routing Algorithm
Dijkstra’s algorithm• net topology, link costs
known to all nodes—accomplished via “link
state broadcast” —all nodes have same
info• computes least cost paths
from one node (‘source”) to all other nodes—gives forwarding table
for that node• iterative: after k iterations,
know least cost path to k dest.’s
Notation:• c(x,y): link cost from node
x to y; = ∞ if not direct neighbors
• D(v): current value of cost of path from source to dest. v
• p(v): predecessor node along path from source to v
• N': set of nodes whose least cost path definitively known
Dijsktra’s Algorithm
1 Initialization: 2 N' = {u} 3 for all nodes v 4 if v adjacent to u 5 then D(v) = c(u,v) 6 else D(v) = ∞ 7 8 Loop 9 find w not in N' such that D(w) is a minimum 10 add w to N' 11 update D(v) for all v adjacent to w and not in N' : 12 D(v) = min( D(v), D(w) + c(w,v) ) 13 /* new cost to v is either old cost to v or known 14 shortest path cost to w plus cost from w to v */ 15 until all nodes in N'
Dijkstra’s algorithm: example
Step012345
N'u
uxuxy
uxyvuxyvw
uxyvwz
D(v),p(v)2,u2,u2,u
D(w),p(w)5,u4,x3,y3,y
D(x),p(x)1,u
D(y),p(y)∞
2,x
D(z),p(z)∞ ∞
4,y4,y4,y
u
yx
wv
z2
2
13
1
1
2
53
5
Dijkstra’s algorithm, discussion
Algorithm complexity: n nodes• each iteration: need to check all nodes, w, not in N• n(n+1)/2 comparisons: O(n2)• more efficient implementations possible: O(nlogn)
Oscillations possible:• e.g., link cost = amount of carried traffic
A
D
C
B1 1+e
e0
e
1 1
0 0
A
D
C
B2+e 0
001+e1
A
D
C
B0 2+e
1+e10 0
A
D
C
B2+e 0
e01+e1
initially… recompute
routing… recompute … recompute
Distance Vector Algorithm (1)
Bellman-Ford Equation (dynamic programming)
Definedx(y) := cost of least-cost path from x to y
Then
dx(y) = min {c(x,v) + dv(y) }
where min is taken over all neighbors of x
Bellman-Ford example (2)
u
yx
wv
z2
2
13
1
1
2
53
5Clearly, dv(z) = 5, dx(z) = 3, dw(z) = 3
du(z) = min { c(u,v) + dv(z), c(u,x) + dx(z), c(u,w) + dw(z) } = min {2 + 5, 1 + 3, 5 + 3} = 4
Node that achieves minimum is nexthop in shortest path ➜ forwarding table
B-F equation says:
Distance Vector Algorithm (3)
• Dx(y) = estimate of least cost from x to y
• Distance vector: Dx = [Dx(y): y є N ]
• Node x knows cost to each neighbor v: c(x,v)
• Node x maintains Dx = [Dx(y): y є N ]
• Node x also maintains its neighbors’ distance vectors—For each neighbor v, x maintains
Dv = [Dv(y): y є N ]
Distance vector algorithm (4)
Basic idea: • Each node periodically sends its own distance
vector estimate to neighbors• When node a node x receives new DV estimate
from neighbor, it updates its own DV using B-F equation:
Dx(y) ← minv{c(x,v) + Dv(y)} for each node y ∊ N
• Under minor, natural conditions, the estimate Dx(y) converge the actual least cost dx(y)
Distance Vector Algorithm (5)
Iterative, asynchronous: each local iteration caused by:
• local link cost change • DV update message from
neighbor
Distributed:• each node notifies
neighbors only when its DV changes— neighbors then notify
their neighbors if necessary
wait for (change in local link cost of msg from neighbor)
recompute estimates
if DV to any dest has
changed, notify neighbors
Each node:
x y z
xyz
0 2 7
∞ ∞ ∞∞ ∞ ∞
from
cost to
from
from
x y z
xyz
0 2 3
from
cost tox y z
xyz
0 2 3
from
cost to
x y z
xyz
∞ ∞
∞ ∞ ∞
cost tox y z
xyz
0 2 7
from
cost to
x y z
xyz
0 2 3
from
cost to
x y z
xyz
0 2 3
from
cost tox y z
xyz
0 2 7
from
cost to
x y z
xyz
∞ ∞ ∞7 1 0
cost to
∞2 0 1
∞ ∞ ∞
2 0 17 1 0
2 0 17 1 0
2 0 13 1 0
2 0 13 1 0
2 0 1
3 1 0
2 0 1
3 1 0
time
x z12
7
y
node x table
node y table
node z table
Dx(y) = min{c(x,y) + Dy(y), c(x,z) + Dz(y)} = min{2+0 , 7+1} = 2
Dx(z) = min{c(x,y) + Dy(z), c(x,z) + Dz(z)} = min{2+1 , 7+0} = 3
Distance Vector: link cost changes
Link cost changes:• node detects local link cost
change • updates routing info, recalculates
distance vector• if DV changes, notify neighbors
“goodnews travelsfast”
x z14
50
y1
At time t0, y detects the link-cost change, updates its DV, and informs its neighbors.
At time t1, z receives the update from y and updates its table. It computes a new least cost to x and sends its neighbors its DV.
At time t2, y receives z’s update and updates its distance table. y’s least costs do not change and hence y does not send any message to z.
Distance Vector: link cost changesLink cost changes:• good news travels fast • bad news travels slow - “count to infinity” problem!• 44 iterations before algorithm stabilizes: see text
Poissoned reverse: • If Z routes through Y to get to X :
— Z tells Y its (Z’s) distance to X is infinite (so Y won’t route to X via Z)
• will this completely solve count to infinity problem?
x z14
50
y60
Comparison of LS and DV algorithms
Message complexity• LS: with n nodes, E links,
O(nE) msgs sent • DV: exchange between
neighbors only—convergence time varies
Speed of Convergence• LS: O(n2) algorithm requires
O(nE) msgs—may have oscillations
• DV: convergence time varies—may be routing loops—count-to-infinity problem
Robustness: what happens if router malfunctions?
LS: —node can advertise
incorrect link cost—each node computes
only its own table
DV:—DV node can advertise
incorrect path cost—each node’s table used
by others • error propagate thru
network
Hierarchical Routing
scale: with 200 million destinations:
• can’t store all dest’s in routing tables!
• routing table exchange would swamp links!
administrative autonomy
• internet = network of networks
• each network admin may want to control routing in its own network
Our routing study thus far - idealization • all routers identical• network “flat”… not true in practice
Hierarchical Routing
• aggregate routers into regions, “autonomous systems” (AS)
• routers in same AS run same routing protocol—“intra-AS” routing
protocol— routers in different AS
can run different intra-AS routing protocol
Gateway router• Direct link to router in
another AS
3b
1d
3a
1c2aAS3
AS1
AS21a
2c2b
1b
Intra-ASRouting algorithm
Inter-ASRouting algorithm
Forwardingtable
3c
Interconnected ASes
• Forwarding table is configured by both intra- and inter-AS routing algorithm—Intra-AS sets entries
for internal dests—Inter-AS & Intra-As
sets entries for external dests
3b
1d
3a
1c2aAS3
AS1
AS21a
2c2b
1b
3c
Inter-AS tasks• Suppose router in
AS1 receives datagram for which dest is outside of AS1—Router should forward
packet towards on of the gateway routers, but which one?
AS1 needs:1. to learn which dests
are reachable through AS2 and which through AS3
2. to propagate this reachability info to all routers in AS1
Job of inter-AS routing!
Example: Setting forwarding table in router 1d
• Suppose AS1 learns from the inter-AS protocol that subnet x is reachable from AS3 (gateway 1c) but not from AS2.
• Inter-AS protocol propagates reachability info to all internal routers.
• Router 1d determines from intra-AS routing info that its interface I is on the least cost path to 1c.
• Puts in forwarding table entry (x,I).
Learn from inter-AS protocol that subnet x is reachable via multiple gateways
Use routing infofrom intra-AS
protocol to determine
costs of least-cost paths to each
of the gateways
Hot potato routing:Choose the
gatewaythat has the
smallest least cost
Determine fromforwarding table the interface I that leads
to least-cost gateway. Enter (x,I) in
forwarding table
Example: Choosing among multiple ASes
• Now suppose AS1 learns from the inter-AS protocol that subnet x is reachable from AS3 and from AS2.
• To configure forwarding table, router 1d must determine towards which gateway it should forward packets for dest x.
• This is also the job on inter-AS routing protocol!• Hot potato routing: send packet towards closest of
two routers.
Intra-AS Routing
• Also known as Interior Gateway Protocols (IGP)• Most common Intra-AS routing protocols:
—RIP: Routing Information Protocol
—OSPF: Open Shortest Path First
—IGRP: Interior Gateway Routing Protocol (Cisco proprietary)
RIP ( Routing Information Protocol)
• Distance vector algorithm• Included in BSD-UNIX Distribution in 1982• Distance metric: # of hops (max = 15 hops)
DC
BA
u v
w
x
yz
destination hops u 1 v 2 w 2 x 3 y 3 z 2
RIP advertisements
• Distance vectors: exchanged among neighbors every 30 sec via Response Message (also called advertisement)
• Each advertisement: list of up to 25 destination nets within AS
RIP: Example
Destination Network Next Router Num. of hops to dest. w A 2
y B 2 z B 7
x -- 1…. …. ....
w x y
z
A
C
D B
Routing table in D
RIP: Example
Destination Network Next Router Num. of hops to dest. w A 2
y B 2 z B A 7 5
x -- 1…. …. ....Routing table in D
w x y
z
A
C
D B
Dest Next hops w - - x - - z C 4 …. … ...
Advertisementfrom A to D
RIP: Link Failure and Recovery If no advertisement heard after 180 sec -->
neighbor/link declared dead—routes via neighbor invalidated—new advertisements sent to neighbors—neighbors in turn send out new advertisements
(if tables changed)—link failure info quickly propagates to entire net—poison reverse used to prevent ping-pong
loops (infinite distance = 16 hops)
RIP Table processing
• RIP routing tables managed by application-level process called route-d (daemon)
• advertisements sent in UDP packets, periodically repeated
physical
link
network forwarding (IP) table
Transprt (UDP)
routed
physical
link
network (IP)
Transprt (UDP)
routed
forwardingtable
OSPF (Open Shortest Path First)
• “open”: publicly available• Uses Link State algorithm
—LS packet dissemination—Topology map at each node—Route computation using Dijkstra’s algorithm
• OSPF advertisement carries one entry per neighbor router
• Advertisements disseminated to entire AS (via flooding)—Carried in OSPF messages directly over IP (rather than
TCP or UDP
OSPF “advanced” features (not in RIP)
• Security: all OSPF messages authenticated (to prevent malicious intrusion)
• Multiple same-cost paths allowed (only one path in RIP)
• For each link, multiple cost metrics for different TOS (e.g., satellite link cost set “low” for best effort; high for real time)
• Integrated uni- and multicast support: —Multicast OSPF (MOSPF) uses same topology
data base as OSPF• Hierarchical OSPF in large domains.
Hierarchical OSPF
• Two-level hierarchy: local area, backbone.—Link-state advertisements only in area —each nodes has detailed area topology; only know
direction (shortest path) to nets in other areas.• Area border routers: “summarize” distances to
nets in own area, advertise to other Area Border routers.
• Backbone routers: run OSPF routing limited to backbone.
• Boundary routers: connect to other AS’s.
Internet inter-AS routing: BGP
• BGP (Border Gateway Protocol): the de facto standard
• BGP provides each AS a means to:1. Obtain subnet reachability information from
neighboring ASs.2. Propagate the reachability information to all
routers internal to the AS.3. Determine “good” routes to subnets based on
reachability information and policy.
• Allows a subnet to advertise its existence to rest of the Internet: “I am here”
BGP basics• Pairs of routers (BGP peers) exchange routing info over
semi-permanent TCP conctns: BGP sessions• Note that BGP sessions do not correspond to physical links.• When AS2 advertises a prefix to AS1, AS2 is promising it
will forward any datagrams destined to that prefix towards the prefix.— AS2 can aggregate prefixes in its advertisement
3b
1d
3a
1c2aAS3
AS1
AS21a
2c
2b
1b
3c
eBGP session
iBGP session
Distributing reachability info• With eBGP session between 3a and 1c, AS3 sends prefix
reachability info to AS1.• 1c can then use iBGP do distribute this new prefix reach
info to all routers in AS1• 1b can then re-advertise the new reach info to AS2 over
the 1b-to-2a eBGP session• When router learns about a new prefix, it creates an
entry for the prefix in its forwarding table.
3b
1d
3a
1c2aAS3
AS1
AS21a
2c
2b
1b
3c
eBGP session
iBGP session
Path attributes & BGP routes
• When advertising a prefix, advert includes BGP attributes. —prefix + attributes = “route”
• Two important attributes:—AS-PATH: contains the ASs through which the advert for
the prefix passed: AS 67 AS 17 —NEXT-HOP: Indicates the specific internal-AS router to
next-hop AS. (There may be multiple links from current AS to next-hop-AS.)
• When gateway router receives route advert, uses import policy to accept/decline.
BGP route selection
• Router may learn about more than 1 route to some prefix. Router must select route.
• Elimination rules:1. Local preference value attribute: policy
decision2. Shortest AS-PATH 3. Closest NEXT-HOP router: hot potato routing4. Additional criteria
BGP messages
• BGP messages exchanged using TCP.• BGP messages:
—OPEN: opens TCP connection to peer and authenticates sender
—UPDATE: advertises new path (or withdraws old)
—KEEPALIVE keeps connection alive in absence of UPDATES; also ACKs OPEN request
—NOTIFICATION: reports errors in previous msg; also used to close connection
BGP routing policy
Figure 4.5-BGPnew: a simple BGP scenario
A
B
C
W X
Y
legend:
customer network:
provider network
• A,B,C are provider networks• X,W,Y are customer (of provider networks)• X is dual-homed: attached to two networks
—X does not want to route from B via X to C—.. so X will not advertise to B a route to C
BGP routing policy (2)
Figure 4.5-BGPnew: a simple BGP scenario
A
B
C
W X
Y
legend:
customer network:
provider network
• A advertises to B the path AW • B advertises to X the path BAW • Should B advertise to C the path BAW?
—No way! B gets no “revenue” for routing CBAW since neither W nor C are B’s customers
—B wants to force C to route to w via A—B wants to route only to/from its customers!
Why different Intra- and Inter-AS routing ?
Policy: • Inter-AS: admin wants control over how its traffic
routed, who routes through its net. • Intra-AS: single admin, so no policy decisions
needed
Scale:• hierarchical routing saves table size, reduced
update trafficPerformance: • Intra-AS: can focus on performance• Inter-AS: policy may dominate over performance